Block #215,046

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 8:21:27 PM · Difficulty 9.9248 · 6,588,714 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc7b84e772c939cd5aaa5352df2f09ac312c67b55909b5e89aed8195ac268d91

View on Chainz ↗

Height

#215,046

Difficulty

9.924846

Transactions

Size

724 B

Version

Bits

09ecc2bc

Nonce

9,525

Timestamp

10/17/2013, 8:21:27 PM

Confirmations

6,588,714

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

1a1714473391bb1f9cf43e7c7977a0c58ce9f86ede7130f38a26e83bcb11b869

Transactions (2)

Coinbase2670a132311131…2cad87742d68e4

1 in → 1 out10.1500 XPM109 B

AH8MuWec…2bVG62mK

c24b10e28e327a…a5fb72e790530d

3 in → 2 out350.0100 XPM522 B

Ac7RAQMV…nKWU2GLU AdzGctTf…vfHWrkn1

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.

4.446 × 10¹⁰²(103-digit number)

44464104999192101890…73306149556846074879

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

4.446 × 10¹⁰²(103-digit number)

44464104999192101890…73306149556846074879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.446 × 10¹⁰²(103-digit number)

44464104999192101890…73306149556846074881

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

8.892 × 10¹⁰²(103-digit number)

88928209998384203780…46612299113692149759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.892 × 10¹⁰²(103-digit number)

88928209998384203780…46612299113692149761

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

1.778 × 10¹⁰³(104-digit number)

17785641999676840756…93224598227384299519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.778 × 10¹⁰³(104-digit number)

17785641999676840756…93224598227384299521

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

3.557 × 10¹⁰³(104-digit number)

35571283999353681512…86449196454768599039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.557 × 10¹⁰³(104-digit number)

35571283999353681512…86449196454768599041

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

7.114 × 10¹⁰³(104-digit number)

71142567998707363024…72898392909537198079

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