Block #181,354

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/26/2013, 12:34:51 PM · Difficulty 9.8597 · 6,627,280 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e695847d1c76727322481a6b29f2c867444c697b3971884d1c9f88d4d4041ce7

View on Chainz ↗

Height

#181,354

Difficulty

9.859735

Transactions

Size

651 B

Version

Bits

09dc17a0

Nonce

30,925

Timestamp

9/26/2013, 12:34:51 PM

Confirmations

6,627,280

Mined by

⛏️ P2SHAemeoLAfHPNy7vp3pWu3MtiRjgZJjxPuF9

Merkle Root

ac401377eb69a27c16dbe71484cf8c311555f708e46e2e198a7d7c8698e0c55e

Transactions (3)

Coinbase663666182624a6…c059e6a79b0baf

1 in → 1 out10.2900 XPM109 B

AemeoLAf…ZJjxPuF9

72fd6021048a02…d19c6436bba3ae

1 in → 2 out10.2500 XPM226 B

AcBo3HDH…pFMzyv2A ATvzd4gx…UmcMEgSR

2319186b993561…308eeabd8bc0ad

1 in → 2 out2.7943 XPM225 B

AUcwm7fj…mwWHgFxW AP4exjFF…2JJqgYei

Prime Chain Origin

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

1.717 × 10⁹⁷(98-digit number)

17170855907055132127…79916447261076853759

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.717 × 10⁹⁷(98-digit number)

17170855907055132127…79916447261076853759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.717 × 10⁹⁷(98-digit number)

17170855907055132127…79916447261076853761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.434 × 10⁹⁷(98-digit number)

34341711814110264254…59832894522153707519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.434 × 10⁹⁷(98-digit number)

34341711814110264254…59832894522153707521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.868 × 10⁹⁷(98-digit number)

68683423628220528509…19665789044307415039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.868 × 10⁹⁷(98-digit number)

68683423628220528509…19665789044307415041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.373 × 10⁹⁸(99-digit number)

13736684725644105701…39331578088614830079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.373 × 10⁹⁸(99-digit number)

13736684725644105701…39331578088614830081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.747 × 10⁹⁸(99-digit number)

27473369451288211403…78663156177229660159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #181,354

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