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Block #62,488

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 7:43:01 PM Β· Difficulty 8.9765 Β· 6,732,566 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
62dc3f7407c6a9fabb003c037046cdeea4a8bb8dc36b9b3d9a138ccabc18eefa
View on Chainz β†—

Height

#62,488

Difficulty

8.976508

Transactions

1

Size

200 B

Version

2

Bits

08f9fc6a

Nonce

401

Timestamp

7/18/2013, 7:43:01 PM

Confirmations

6,732,566

Mined by

⛏️ P2SHAGCUbq6Mxc7yQk3kiL3txXdSCgQSxWg1oL

Merkle Root

78d0b3d523e0d00fe4aebab541b4a0a54954877b9cda557098cc4535cefdcda6
Transactions (1)
Coinbase78d0b3d523e0d0…cc4535cefdcda6
1 in β†’ 1 out12.3900 XPM110 B
AGCUbq6M…QSxWg1oL
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.199 Γ— 10⁹⁡(96-digit number)
31996888673362517574…56689935489114694259
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.199 Γ— 10⁹⁡(96-digit number)
31996888673362517574…56689935489114694259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.199 Γ— 10⁹⁡(96-digit number)
31996888673362517574…56689935489114694261
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
6.399 Γ— 10⁹⁡(96-digit number)
63993777346725035148…13379870978229388519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.399 Γ— 10⁹⁡(96-digit number)
63993777346725035148…13379870978229388521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.279 Γ— 10⁹⁢(97-digit number)
12798755469345007029…26759741956458777039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.279 Γ— 10⁹⁢(97-digit number)
12798755469345007029…26759741956458777041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.559 Γ— 10⁹⁢(97-digit number)
25597510938690014059…53519483912917554079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.559 Γ— 10⁹⁢(97-digit number)
25597510938690014059…53519483912917554081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,604,473 XPMΒ·at block #6,795,053 Β· updates every 60s
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