Block #156,914

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/9/2013, 6:48:40 AM · Difficulty 9.8688 · 6,646,737 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a556decbf476d1147de81e45abc7a1bdea13ddc2c933b92b54e27e5b30e5a66

View on Chainz ↗

Height

#156,914

Difficulty

9.868788

Transactions

Size

664 B

Version

Bits

09de68e3

Nonce

7,737

Timestamp

9/9/2013, 6:48:40 AM

Confirmations

6,646,737

Mined by

⛏️ P2SHAGHcDaXo7XFueagDMQYKDpidxjb2wLi8Ht

Merkle Root

b6c56c35beeb31398117699460ea1f0bd2c228c43472d6b254c8351f617dcb70

Transactions (3)

Coinbasedccd7841670f94…ad1ee1b693c5ba

1 in → 1 out10.2700 XPM109 B

AGHcDaXo…b2wLi8Ht

6c0c7e87afb3f0…04cce0327f186c

2 in → 1 out20.5900 XPM272 B

APeDAcqo…ytsjeXth

2cee5f39dce4d0…9bb7a0344fc7a5

1 in → 1 out195.0300 XPM193 B

AbxSykSg…BX71twYi

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.

2.459 × 10⁹⁴(95-digit number)

24597126461554178088…94158226308759978659

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

2.459 × 10⁹⁴(95-digit number)

24597126461554178088…94158226308759978659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.459 × 10⁹⁴(95-digit number)

24597126461554178088…94158226308759978661

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

4.919 × 10⁹⁴(95-digit number)

49194252923108356176…88316452617519957319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.919 × 10⁹⁴(95-digit number)

49194252923108356176…88316452617519957321

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

9.838 × 10⁹⁴(95-digit number)

98388505846216712352…76632905235039914639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.838 × 10⁹⁴(95-digit number)

98388505846216712352…76632905235039914641

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

1.967 × 10⁹⁵(96-digit number)

19677701169243342470…53265810470079829279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.967 × 10⁹⁵(96-digit number)

19677701169243342470…53265810470079829281

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

3.935 × 10⁹⁵(96-digit number)

39355402338486684941…06531620940159658559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.935 × 10⁹⁵(96-digit number)

39355402338486684941…06531620940159658561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — 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

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 × 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