Block #243,416

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 7:08:44 AM · Difficulty 9.9614 · 6,589,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a80b5b0ae0dd2c5f8af9331c9e33d5f40b0494eeb26710c585062b1e95c6ff71

View on Chainz ↗

Height

#243,416

Difficulty

9.961419

Transactions

Size

1.93 KB

Version

Bits

09f61f92

Nonce

72,143

Timestamp

11/4/2013, 7:08:44 AM

Confirmations

6,589,496

Mined by

⛏️ RwGAKFMENK8Y83ntTmGeVC63vAJZ8b6knxLfH

Merkle Root

98aede477dbc52d6e93c0aafcb2b2424de0d71a1671bdb87cc2405b120bbafc9

Transactions (2)

Coinbasedc7c734e1d3985…3f03b84a0d6b94

1 in → 47 out10.0400 XPM1.62 KB

AKFMENK8…b6knxLfH ANpPrsJp…YzdEphWb Acs9SHrk…QJSB8SFG APVGazMT…cDCk2nwA AJzWx2VD…j4ZSMit5

58d3034c91c624…5af50af9d965ca

1 in → 2 out7.2077 XPM225 B

ARskhKeb…UgDvvX9P AW6bXuXS…tLwLFwMh

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.

6.962 × 10⁹²(93-digit number)

69626462122474839611…87680900765423155199

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

6.962 × 10⁹²(93-digit number)

69626462122474839611…87680900765423155199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.962 × 10⁹²(93-digit number)

69626462122474839611…87680900765423155201

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

1.392 × 10⁹³(94-digit number)

13925292424494967922…75361801530846310399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.392 × 10⁹³(94-digit number)

13925292424494967922…75361801530846310401

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

2.785 × 10⁹³(94-digit number)

27850584848989935844…50723603061692620799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.785 × 10⁹³(94-digit number)

27850584848989935844…50723603061692620801

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

5.570 × 10⁹³(94-digit number)

55701169697979871689…01447206123385241599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.570 × 10⁹³(94-digit number)

55701169697979871689…01447206123385241601

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

1.114 × 10⁹⁴(95-digit number)

11140233939595974337…02894412246770483199

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

Block #243,416

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