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Block #1,266,572

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/4/2015, 10:19:14 AM Β· Difficulty 10.8197 Β· 5,550,520 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64eaba4a71f50a99517026a7f1469ffe4066b65be97de0f0ad018c39676ad16a
View on Chainz β†—

Height

#1,266,572

Difficulty

10.819676

Transactions

2

Size

1.14 KB

Version

2

Bits

0ad1d64c

Nonce

564,554,942

Timestamp

10/4/2015, 10:19:14 AM

Confirmations

5,550,520

Mined by

⛏️ P2SHASH7p7XjQitVniKg5th8Hid5VvaS8vKWBZ

Merkle Root

e8e9454e0a615c977bede938bd0e14e7a9c067716e9c62fac208b77ff5ad7632
Transactions (2)
Coinbase5a1d4579018313…ea0f7c19a09980
1 in β†’ 1 out8.5400 XPM110 B
ASH7p7Xj…aS8vKWBZ
ded173ee868566…79766f1d7a81ef
6 in β†’ 2 out39.8000 XPM964 B
ASsNcupd…wCg7kK67AeXSFDp2…rU86AmhP
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.

1.053 Γ— 10⁹⁢(97-digit number)
10536295467336734674…44859491639103231999
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
1.053 Γ— 10⁹⁢(97-digit number)
10536295467336734674…44859491639103231999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.053 Γ— 10⁹⁢(97-digit number)
10536295467336734674…44859491639103232001
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
2.107 Γ— 10⁹⁢(97-digit number)
21072590934673469348…89718983278206463999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.107 Γ— 10⁹⁢(97-digit number)
21072590934673469348…89718983278206464001
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
4.214 Γ— 10⁹⁢(97-digit number)
42145181869346938696…79437966556412927999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.214 Γ— 10⁹⁢(97-digit number)
42145181869346938696…79437966556412928001
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
8.429 Γ— 10⁹⁢(97-digit number)
84290363738693877393…58875933112825855999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.429 Γ— 10⁹⁢(97-digit number)
84290363738693877393…58875933112825856001
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
1.685 Γ— 10⁹⁷(98-digit number)
16858072747738775478…17751866225651711999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.685 Γ— 10⁹⁷(98-digit number)
16858072747738775478…17751866225651712001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,780,773 XPMΒ·at block #6,817,091 Β· updates every 60s
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