Block #2,601,725

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/5/2018, 8:04:52 PM · Difficulty 11.3160 · 4,236,851 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c7e1303a32e8660bcae70c120fabad9614a941fa1ecd28731508a95b49a37da

View on Chainz ↗

Height

#2,601,725

Difficulty

11.315988

Transactions

Size

618 B

Version

Bits

0b50e492

Nonce

338,034,594

Timestamp

4/5/2018, 8:04:52 PM

Confirmations

4,236,851

Mined by

⛏️ P2SHAR3PCEaGXRpCRWiLpKQUpAT8hKSiQPkrJe

Merkle Root

4c9b056d00491269db55af7082153c59157d2b79b759faf3cc8988cf5c3752a8

Transactions (3)

Coinbase39946dce591cca…b7621d82b26260

1 in → 1 out7.8200 XPM110 B

AR3PCEaG…SiQPkrJe

513c425125699a…32e2b7da4399ec

1 in → 2 out7.7800 XPM191 B

AXW9Eb93…Uwpoug6D AWp4iAg7…FUBLEm8x

bb2f0cc0577b0c…89cb3f668021d1

1 in → 2 out2.6665 XPM226 B

AG677DtN…mfvDh1yo AXRjjuok…HYxq4Hfc

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.

2.254 × 10⁹⁶(97-digit number)

22540219330847184391…23386526498939711999

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

2.254 × 10⁹⁶(97-digit number)

22540219330847184391…23386526498939711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.254 × 10⁹⁶(97-digit number)

22540219330847184391…23386526498939712001

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

4.508 × 10⁹⁶(97-digit number)

45080438661694368782…46773052997879423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.508 × 10⁹⁶(97-digit number)

45080438661694368782…46773052997879424001

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

9.016 × 10⁹⁶(97-digit number)

90160877323388737565…93546105995758847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.016 × 10⁹⁶(97-digit number)

90160877323388737565…93546105995758848001

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

1.803 × 10⁹⁷(98-digit number)

18032175464677747513…87092211991517695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.803 × 10⁹⁷(98-digit number)

18032175464677747513…87092211991517696001

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

3.606 × 10⁹⁷(98-digit number)

36064350929355495026…74184423983035391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.606 × 10⁹⁷(98-digit number)

36064350929355495026…74184423983035392001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.212 × 10⁹⁷(98-digit number)

72128701858710990052…48368847966070783999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,601,725

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