Block #2,130,014

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2017, 3:36:20 AM · Difficulty 10.9094 · 4,707,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bac4a3d1ec2589703b2cf04ac1ffbd28435078328131ce52cc4ccc09b4108cd4

View on Chainz ↗

Height

#2,130,014

Difficulty

10.909423

Transactions

Size

426 B

Version

Bits

0ae8cff2

Nonce

420,880,249

Timestamp

5/24/2017, 3:36:20 AM

Confirmations

4,707,504

Mined by

⛏️ P2SHANzChrvCBtXDKsozFHKf3RDLnxAwLnJ9UK

Merkle Root

06428428027f599f7ddfdc16b736b0e93707cbc64c73c04f8b798614824679f7

Transactions (2)

Coinbasea9835c7dc1ecc0…a81a688a0a8dba

1 in → 1 out8.4000 XPM110 B

ANzChrvC…AwLnJ9UK

9d37a9e7501a96…262107fa10ef4d

1 in → 2 out203264.5159 XPM225 B

AGch1BwS…2izGfXD8 Aewa9Ext…5L2uuntj

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.

1.057 × 10⁹⁸(99-digit number)

10575128740624613930…28486585044395458559

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

1.057 × 10⁹⁸(99-digit number)

10575128740624613930…28486585044395458559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.057 × 10⁹⁸(99-digit number)

10575128740624613930…28486585044395458561

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

2.115 × 10⁹⁸(99-digit number)

21150257481249227860…56973170088790917119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.115 × 10⁹⁸(99-digit number)

21150257481249227860…56973170088790917121

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

4.230 × 10⁹⁸(99-digit number)

42300514962498455720…13946340177581834239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.230 × 10⁹⁸(99-digit number)

42300514962498455720…13946340177581834241

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

8.460 × 10⁹⁸(99-digit number)

84601029924996911441…27892680355163668479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.460 × 10⁹⁸(99-digit number)

84601029924996911441…27892680355163668481

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

1.692 × 10⁹⁹(100-digit number)

16920205984999382288…55785360710327336959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.692 × 10⁹⁹(100-digit number)

16920205984999382288…55785360710327336961

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 #2,130,014

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