Block #236,573

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 1:46:54 PM · Difficulty 9.9479 · 6,562,912 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee8174bfb808d95b869667a46074ffefb7cb3915ae49e4191857f11b3b594075

View on Chainz ↗

Height

#236,573

Difficulty

9.947905

Transactions

Size

1.48 KB

Version

Bits

09f2a9e2

Nonce

84,585

Timestamp

10/31/2013, 1:46:54 PM

Confirmations

6,562,912

Mined by

⛏️ Rr_8'AeLjc3taqj48BJZKRddRpUKxx76Gk5xuJk

Merkle Root

300a2af44f190ea3a6004a027d974152f0126021390033638b0c2c23841cef0c

Transactions (1)

Coinbase300a2af44f190e…0c2c23841cef0c

1 in → 40 out10.0700 XPM1.39 KB

AeLjc3ta…6Gk5xuJk AXz2kWvX…V5ZFCDBd APVGazMT…cDCk2nwA ARpndEmc…Hg792kEk APui4t7L…pz97NdcB

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.

7.113 × 10⁹³(94-digit number)

71135498109544545502…03528799917603852799

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

7.113 × 10⁹³(94-digit number)

71135498109544545502…03528799917603852799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.113 × 10⁹³(94-digit number)

71135498109544545502…03528799917603852801

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

1.422 × 10⁹⁴(95-digit number)

14227099621908909100…07057599835207705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.422 × 10⁹⁴(95-digit number)

14227099621908909100…07057599835207705601

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

2.845 × 10⁹⁴(95-digit number)

28454199243817818201…14115199670415411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.845 × 10⁹⁴(95-digit number)

28454199243817818201…14115199670415411201

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

5.690 × 10⁹⁴(95-digit number)

56908398487635636402…28230399340830822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.690 × 10⁹⁴(95-digit number)

56908398487635636402…28230399340830822401

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

1.138 × 10⁹⁵(96-digit number)

11381679697527127280…56460798681661644799

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