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Block #62,517

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 7:51:57 PM Β· Difficulty 8.9766 Β· 6,747,530 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ff94c4d8c6bf9f20109e4be5447ad77912ba8a13a220a40a35f606d77bdfd007
View on Chainz β†—

Height

#62,517

Difficulty

8.976579

Transactions

2

Size

359 B

Version

2

Bits

08fa0112

Nonce

133

Timestamp

7/18/2013, 7:51:57 PM

Confirmations

6,747,530

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

a69be5f0715fe116d9fd1297d99db9109b24502ff1772c3d8671b48447e277dc
Transactions (2)
Coinbasecab3d621468477…632ae114d02cb5
1 in β†’ 1 out12.4000 XPM110 B
AV6P7enU…VLHeixvR
9a8dd663984da7…feb39a079252fe
1 in β†’ 1 out13.1000 XPM158 B
ANUq464L…3RdVWkUR
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.

2.117 Γ— 10⁹⁢(97-digit number)
21179208876703887914…62920664618017124399
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
2.117 Γ— 10⁹⁢(97-digit number)
21179208876703887914…62920664618017124399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.117 Γ— 10⁹⁢(97-digit number)
21179208876703887914…62920664618017124401
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
4.235 Γ— 10⁹⁢(97-digit number)
42358417753407775829…25841329236034248799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.235 Γ— 10⁹⁢(97-digit number)
42358417753407775829…25841329236034248801
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
8.471 Γ— 10⁹⁢(97-digit number)
84716835506815551659…51682658472068497599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.471 Γ— 10⁹⁢(97-digit number)
84716835506815551659…51682658472068497601
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
1.694 Γ— 10⁹⁷(98-digit number)
16943367101363110331…03365316944136995199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.694 Γ— 10⁹⁷(98-digit number)
16943367101363110331…03365316944136995201
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:57,724,448 XPMΒ·at block #6,810,046 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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