Block #219,099

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 8:07:56 AM · Difficulty 9.9318 · 6,576,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7a35e66dcb4e7c6ae8703ced451c72746f86b9fc2284273ca3e251dcd8a1332

View on Chainz ↗

Height

#219,099

Difficulty

9.931750

Transactions

Size

1.71 KB

Version

Bits

09ee872c

Nonce

33,393

Timestamp

10/20/2013, 8:07:56 AM

Confirmations

6,576,455

Mined by

⛏️ P2SHAJWARb6HFjoLazGPbnKB5vLV3SNR8M7MUE

Merkle Root

89a3ca048d7828c663b2e0a7aa25e10b69a189a92a3682faf97dbd3fd9e74b2e

Transactions (4)

Coinbasee4eef7bb732010…e8e9493a1dfe83

1 in → 1 out10.1600 XPM109 B

AJWARb6H…NR8M7MUE

909c51d624a5e1…10e7b4201e3676

1 in → 2 out10.1300 XPM225 B

AYKVeNA9…BbJrTDhi Aahbga5N…5WAmuvVo

b5b48ce8df5197…dd04e988dd70d6

6 in → 8 out26.0132 XPM1.08 KB

AWk3tNVN…AM1VtV3G AZ4QAejN…gwqGZDtJ AVKfZvtY…sCa4NTcM AXLJfptX…uPWXiXzg Acs9SHrk…QJSB8SFG

1d60b7e0a565df…6412e4d7e692b5

1 in → 2 out6.7551 XPM226 B

AJ2ubz2o…WoHUkXkm AMmGeXac…8N1iWEtv

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.

2.644 × 10⁹²(93-digit number)

26447687891140289239…32513095468482714499

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

2.644 × 10⁹²(93-digit number)

26447687891140289239…32513095468482714499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.644 × 10⁹²(93-digit number)

26447687891140289239…32513095468482714501

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

5.289 × 10⁹²(93-digit number)

52895375782280578479…65026190936965428999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.289 × 10⁹²(93-digit number)

52895375782280578479…65026190936965429001

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

1.057 × 10⁹³(94-digit number)

10579075156456115695…30052381873930857999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.057 × 10⁹³(94-digit number)

10579075156456115695…30052381873930858001

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

2.115 × 10⁹³(94-digit number)

21158150312912231391…60104763747861715999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.115 × 10⁹³(94-digit number)

21158150312912231391…60104763747861716001

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

4.231 × 10⁹³(94-digit number)

42316300625824462783…20209527495723431999

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