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Block #2,129,398

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/23/2017, 4:21:02 PM Β· Difficulty 10.9104 Β· 4,701,647 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9d93323f724aed9b1faa1a962df56253745dbe34095fdf8d4b1917f007dfe1dd
View on Chainz β†—

Height

#2,129,398

Difficulty

10.910442

Transactions

1

Size

210 B

Version

2

Bits

0ae912b8

Nonce

466,532,102

Timestamp

5/23/2017, 4:21:02 PM

Confirmations

4,701,647

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

9035ee3116a2c485285e4316bc2d8fada0197f8b7402e86cbfca3f5a6f28887f
Transactions (1)
Coinbase9035ee3116a2c4…ca3f5a6f28887f
1 in β†’ 1 out8.3900 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.315 Γ— 10⁹⁹(100-digit number)
13152776709476821482…54935285431139696639
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
1.315 Γ— 10⁹⁹(100-digit number)
13152776709476821482…54935285431139696639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.315 Γ— 10⁹⁹(100-digit number)
13152776709476821482…54935285431139696641
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
2.630 Γ— 10⁹⁹(100-digit number)
26305553418953642964…09870570862279393279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.630 Γ— 10⁹⁹(100-digit number)
26305553418953642964…09870570862279393281
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
5.261 Γ— 10⁹⁹(100-digit number)
52611106837907285928…19741141724558786559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.261 Γ— 10⁹⁹(100-digit number)
52611106837907285928…19741141724558786561
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
1.052 Γ— 10¹⁰⁰(101-digit number)
10522221367581457185…39482283449117573119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.052 Γ— 10¹⁰⁰(101-digit number)
10522221367581457185…39482283449117573121
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
2.104 Γ— 10¹⁰⁰(101-digit number)
21044442735162914371…78964566898235146239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.104 Γ— 10¹⁰⁰(101-digit number)
21044442735162914371…78964566898235146241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,892,498 XPMΒ·at block #6,831,044 Β· updates every 60s
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