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Block #636,555

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 7/17/2014, 12:39:20 AM Β· Difficulty 10.9637 Β· 6,190,284 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
940b413e82f8c188fbc8c58410d240db937ba31d6b3db364f1fff8bb62f7f78c
View on Chainz β†—

Height

#636,555

Difficulty

10.963663

Transactions

1

Size

201 B

Version

2

Bits

0af6b2a3

Nonce

70,812

Timestamp

7/17/2014, 12:39:20 AM

Confirmations

6,190,284

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

815dc7e62b062d8f05b5ff9952b0390a05a2f8d6efd81a571bdf7eea11dc23b1
Transactions (1)
Coinbase815dc7e62b062d…df7eea11dc23b1
1 in β†’ 1 out8.3100 XPM110 B
AeKNrjNj…1NEq95Ta
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.299 Γ— 10⁹⁢(97-digit number)
92993781310587585891…99426652399069564479
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
9.299 Γ— 10⁹⁢(97-digit number)
92993781310587585891…99426652399069564479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.299 Γ— 10⁹⁢(97-digit number)
92993781310587585891…99426652399069564481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.859 Γ— 10⁹⁷(98-digit number)
18598756262117517178…98853304798139128959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.859 Γ— 10⁹⁷(98-digit number)
18598756262117517178…98853304798139128961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.719 Γ— 10⁹⁷(98-digit number)
37197512524235034356…97706609596278257919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.719 Γ— 10⁹⁷(98-digit number)
37197512524235034356…97706609596278257921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
7.439 Γ— 10⁹⁷(98-digit number)
74395025048470068713…95413219192556515839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.439 Γ— 10⁹⁷(98-digit number)
74395025048470068713…95413219192556515841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.487 Γ— 10⁹⁸(99-digit number)
14879005009694013742…90826438385113031679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.487 Γ— 10⁹⁸(99-digit number)
14879005009694013742…90826438385113031681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.975 Γ— 10⁹⁸(99-digit number)
29758010019388027485…81652876770226063359
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.975 Γ— 10⁹⁸(99-digit number)
29758010019388027485…81652876770226063361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,858,879 XPMΒ·at block #6,826,838 Β· updates every 60s
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