Block #1,351,225

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2015, 5:06:34 PM · Difficulty 10.7958 · 5,458,688 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c15286c2289b2803447e4621dd5377019e053bf99997f0a8fef0b42fcc4e1334

View on Chainz ↗

Height

#1,351,225

Difficulty

10.795811

Transactions

Size

1.55 KB

Version

Bits

0acbba3f

Nonce

2,125,524,168

Timestamp

12/2/2015, 5:06:34 PM

Confirmations

5,458,688

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

18dc026f59d8911e5c3aa3f1acf5ac56ed2888d72e78dbc3ae68d348c5320071

Transactions (2)

Coinbase3d65ccc243b95a…a31b8cd7922d0b

1 in → 1 out8.5900 XPM116 B

AJCEY9yy…tg97E6zm

f378b0353b60e6…97323a51ec1335

1 in → 36 out105.2395 XPM1.35 KB

ATQ2RfSs…yao2HZMj AGSp8xAT…zSfPdQHA AJGzMLu3…YWxgciRq AJHWT6Ae…bhA38DDq AVEYJtbR…Zqkssptv

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.

5.045 × 10⁹⁵(96-digit number)

50456606917546787410…44649500823533129699

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

5.045 × 10⁹⁵(96-digit number)

50456606917546787410…44649500823533129699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.045 × 10⁹⁵(96-digit number)

50456606917546787410…44649500823533129701

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

1.009 × 10⁹⁶(97-digit number)

10091321383509357482…89299001647066259399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.009 × 10⁹⁶(97-digit number)

10091321383509357482…89299001647066259401

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

2.018 × 10⁹⁶(97-digit number)

20182642767018714964…78598003294132518799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.018 × 10⁹⁶(97-digit number)

20182642767018714964…78598003294132518801

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

4.036 × 10⁹⁶(97-digit number)

40365285534037429928…57196006588265037599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.036 × 10⁹⁶(97-digit number)

40365285534037429928…57196006588265037601

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

8.073 × 10⁹⁶(97-digit number)

80730571068074859856…14392013176530075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.073 × 10⁹⁶(97-digit number)

80730571068074859856…14392013176530075201

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

Block #1,351,225

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