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Block #1,794,117

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/5/2016, 7:50:13 PM Β· Difficulty 10.7756 Β· 5,032,807 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bed5314cdcb52005a37593f26ac6c3a4885d9630b2efef05f34f847f4af7b0ca
View on Chainz β†—

Height

#1,794,117

Difficulty

10.775561

Transactions

1

Size

242 B

Version

2

Bits

0ac68b2f

Nonce

768,052,476

Timestamp

10/5/2016, 7:50:13 PM

Confirmations

5,032,807

Mined by

⛏️ jhPrimeminerATd5Bq5SNppozp9HDzLQKxc4KVPcfPgHVj

Merkle Root

7022f6a801bbcc89fd056b3c3062ddffe70f4f6e141f3b187ae2a14b40ed49dd
Transactions (1)
Coinbase7022f6a801bbcc…e2a14b40ed49dd
1 in β†’ 2 out8.6000 XPM152 B
ATd5Bq5S…PcfPgHVjALPu3s2c…EJXLjVFh
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.

1.887 Γ— 10⁹⁡(96-digit number)
18874230773419421670…00982794162789905439
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
1.887 Γ— 10⁹⁡(96-digit number)
18874230773419421670…00982794162789905439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.887 Γ— 10⁹⁡(96-digit number)
18874230773419421670…00982794162789905441
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
3.774 Γ— 10⁹⁡(96-digit number)
37748461546838843341…01965588325579810879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.774 Γ— 10⁹⁡(96-digit number)
37748461546838843341…01965588325579810881
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
7.549 Γ— 10⁹⁡(96-digit number)
75496923093677686683…03931176651159621759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.549 Γ— 10⁹⁡(96-digit number)
75496923093677686683…03931176651159621761
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
1.509 Γ— 10⁹⁢(97-digit number)
15099384618735537336…07862353302319243519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.509 Γ— 10⁹⁢(97-digit number)
15099384618735537336…07862353302319243521
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
3.019 Γ— 10⁹⁢(97-digit number)
30198769237471074673…15724706604638487039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.019 Γ— 10⁹⁢(97-digit number)
30198769237471074673…15724706604638487041
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:57,859,563 XPMΒ·at block #6,826,923 Β· updates every 60s
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