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Block #63,726

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2013, 3:09:59 AM Β· Difficulty 8.9799 Β· 6,735,541 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
960a438b6970365bd27b455be82e3bc4390bcb9a8f72ffc00ab662efe904350b
View on Chainz β†—

Height

#63,726

Difficulty

8.979914

Transactions

2

Size

723 B

Version

2

Bits

08fadba8

Nonce

80

Timestamp

7/19/2013, 3:09:59 AM

Confirmations

6,735,541

Mined by

⛏️ P2SHALhja5Eru9hHPKBw3gECm96LpDuFo3XQuV

Merkle Root

ddee6f87c4834e46ca9c7c3b93961c55136904e600d95434a443878d93fee3c4
Transactions (2)
Coinbasefe3d18b7723a3c…ac679c9e708986
1 in β†’ 1 out12.3900 XPM110 B
ALhja5Er…uFo3XQuV
e198287a001427…811d583066a213
3 in β†’ 2 out47.0443 XPM523 B
AY2ek3A3…Yvkc2puZAW7aqm7z…MZ7TogRx
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.

3.187 Γ— 10⁹⁡(96-digit number)
31878271303037495283…93309133921131903899
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
3.187 Γ— 10⁹⁡(96-digit number)
31878271303037495283…93309133921131903899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.187 Γ— 10⁹⁡(96-digit number)
31878271303037495283…93309133921131903901
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
6.375 Γ— 10⁹⁡(96-digit number)
63756542606074990566…86618267842263807799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.375 Γ— 10⁹⁡(96-digit number)
63756542606074990566…86618267842263807801
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
1.275 Γ— 10⁹⁢(97-digit number)
12751308521214998113…73236535684527615599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.275 Γ— 10⁹⁢(97-digit number)
12751308521214998113…73236535684527615601
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
2.550 Γ— 10⁹⁢(97-digit number)
25502617042429996226…46473071369055231199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.550 Γ— 10⁹⁢(97-digit number)
25502617042429996226…46473071369055231201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.100 Γ— 10⁹⁢(97-digit number)
51005234084859992453…92946142738110462399
Verify on FactorDB β†—Wolfram Alpha β†—

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 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 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 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:57,638,175 XPMΒ·at block #6,799,266 Β· updates every 60s
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