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Block #106,620

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2013, 3:02:04 AM Β· Difficulty 9.6105 Β· 6,702,955 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
965b52ca6791a803f3b9e4e22de363132063e20ec7308354912e96e01c2a3bd0
View on Chainz β†—

Height

#106,620

Difficulty

9.610496

Transactions

2

Size

358 B

Version

2

Bits

099c497d

Nonce

30,939

Timestamp

8/9/2013, 3:02:04 AM

Confirmations

6,702,955

Mined by

⛏️ P2SHAP2sfUxBQckBN9DE9o8ujnks7NEtcugPME

Merkle Root

040aba7b7ebfbef64f0b33f67ed46799bbeb524132f3d2a163ec3b731ffcc4d3
Transactions (2)
Coinbasef19aa7f874200b…d87349b4f665c3
1 in β†’ 1 out10.8200 XPM109 B
AP2sfUxB…EtcugPME
cec8ec11af27cb…726778afc93cc3
1 in β†’ 1 out11.0300 XPM158 B
ATareS7a…5FKKTQVH
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.

7.250 Γ— 10⁹⁢(97-digit number)
72505381601028024262…34792746570806515119
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
7.250 Γ— 10⁹⁢(97-digit number)
72505381601028024262…34792746570806515119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.250 Γ— 10⁹⁢(97-digit number)
72505381601028024262…34792746570806515121
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
1.450 Γ— 10⁹⁷(98-digit number)
14501076320205604852…69585493141613030239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.450 Γ— 10⁹⁷(98-digit number)
14501076320205604852…69585493141613030241
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
2.900 Γ— 10⁹⁷(98-digit number)
29002152640411209704…39170986283226060479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.900 Γ— 10⁹⁷(98-digit number)
29002152640411209704…39170986283226060481
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
5.800 Γ— 10⁹⁷(98-digit number)
58004305280822419409…78341972566452120959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.800 Γ— 10⁹⁷(98-digit number)
58004305280822419409…78341972566452120961
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
1.160 Γ— 10⁹⁸(99-digit number)
11600861056164483881…56683945132904241919
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:57,720,677 XPMΒ·at block #6,809,574 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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