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Block #101,491

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/6/2013, 4:14:22 PM Β· Difficulty 9.4634 Β· 6,700,633 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
36e0168c6cd4088e41d07439c8414fe331989be35ce1060606a1bd52ded2cb80
View on Chainz β†—

Height

#101,491

Difficulty

9.463412

Transactions

2

Size

358 B

Version

2

Bits

0976a226

Nonce

190,395

Timestamp

8/6/2013, 4:14:22 PM

Confirmations

6,700,633

Mined by

⛏️ P2SHAa91xM1voie47yrqooP8dVcUjVXSEFKdcy

Merkle Root

248b5d16573a98643ff1ad0dd7c2e301a8e720eac42e4f843083416920913c0f
Transactions (2)
Coinbasef167e91a9034de…4305defaa6f5d2
1 in β†’ 1 out11.1600 XPM109 B
Aa91xM1v…XSEFKdcy
e4268ab674c803…8ef21f1a944619
1 in β†’ 1 out11.4700 XPM157 B
Ad91bTac…3L6H7xaC
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.

2.178 Γ— 10⁹⁹(100-digit number)
21785792401264179770…75230031842093147819
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
2.178 Γ— 10⁹⁹(100-digit number)
21785792401264179770…75230031842093147819
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.178 Γ— 10⁹⁹(100-digit number)
21785792401264179770…75230031842093147821
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
4.357 Γ— 10⁹⁹(100-digit number)
43571584802528359540…50460063684186295639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.357 Γ— 10⁹⁹(100-digit number)
43571584802528359540…50460063684186295641
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
8.714 Γ— 10⁹⁹(100-digit number)
87143169605056719081…00920127368372591279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.714 Γ— 10⁹⁹(100-digit number)
87143169605056719081…00920127368372591281
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
1.742 Γ— 10¹⁰⁰(101-digit number)
17428633921011343816…01840254736745182559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.742 Γ— 10¹⁰⁰(101-digit number)
17428633921011343816…01840254736745182561
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
3.485 Γ— 10¹⁰⁰(101-digit number)
34857267842022687632…03680509473490365119
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:57,660,995 XPMΒ·at block #6,802,123 Β· updates every 60s
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