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Block #62,208

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 5:46:38 PM Β· Difficulty 8.9757 Β· 6,747,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2aaa48f05dd310fd2ddb10ed8b34d947210147d57d5f28dfb644ac8b1d7d8759
View on Chainz β†—

Height

#62,208

Difficulty

8.975699

Transactions

2

Size

358 B

Version

2

Bits

08f9c769

Nonce

935

Timestamp

7/18/2013, 5:46:38 PM

Confirmations

6,747,599

Mined by

⛏️ P2SHAGJAJsS85GzzR9LE7vkTRhx41bSQ6rgW1w

Merkle Root

106cd9b945d8137b4fd30f8dbd898a855dcbf379124f26d8012fc0256e7d75ce
Transactions (2)
Coinbaseb68ee13a77b622…80059658bcd799
1 in β†’ 1 out12.4100 XPM110 B
AGJAJsS8…SQ6rgW1w
1edca6bfc381e1…4079d8e6dae9cc
1 in β†’ 1 out12.4200 XPM158 B
ALixprTJ…AL6Ff59B
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.

6.201 Γ— 10⁹³(94-digit number)
62011504116038948456…29169641667501131799
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
6.201 Γ— 10⁹³(94-digit number)
62011504116038948456…29169641667501131799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.201 Γ— 10⁹³(94-digit number)
62011504116038948456…29169641667501131801
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
1.240 Γ— 10⁹⁴(95-digit number)
12402300823207789691…58339283335002263599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.240 Γ— 10⁹⁴(95-digit number)
12402300823207789691…58339283335002263601
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
2.480 Γ— 10⁹⁴(95-digit number)
24804601646415579382…16678566670004527199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.480 Γ— 10⁹⁴(95-digit number)
24804601646415579382…16678566670004527201
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
4.960 Γ— 10⁹⁴(95-digit number)
49609203292831158764…33357133340009054399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.960 Γ— 10⁹⁴(95-digit number)
49609203292831158764…33357133340009054401
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
9.921 Γ— 10⁹⁴(95-digit number)
99218406585662317529…66714266680018108799
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:57,722,538 XPMΒ·at block #6,809,806 Β· updates every 60s
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