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Block #1,901,633

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2016, 10:56:02 AM Β· Difficulty 10.7815 Β· 4,922,887 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3118b416b4178f5bdb0ef68b1d6fa0404a7454a470c209c321660d0a4670ed4e
View on Chainz β†—

Height

#1,901,633

Difficulty

10.781517

Transactions

2

Size

1.43 KB

Version

2

Bits

0ac8117c

Nonce

1,510,325,584

Timestamp

12/19/2016, 10:56:02 AM

Confirmations

4,922,887

Mined by

⛏️ P2SHAcfNtr72p7vZzDnbYbjz1tL7Qj5JePnAsQ

Merkle Root

689e8c8d194afeff6f00e318985e5b5de1bb30c69647ec10b935d3964f43e13a
Transactions (2)
Coinbase604498156546db…91d2123db34b95
1 in β†’ 1 out8.6100 XPM109 B
AcfNtr72…5JePnAsQ
b3cd8b58e41ac5…a7ab1a92985099
8 in β†’ 2 out7202.4919 XPM1.23 KB
AGBz9K3B…1HovgLcZAMP7EGhn…hgQDQGEc
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.

1.347 Γ— 10⁹⁡(96-digit number)
13472343311321815102…76532109373511873279
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
1.347 Γ— 10⁹⁡(96-digit number)
13472343311321815102…76532109373511873279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.347 Γ— 10⁹⁡(96-digit number)
13472343311321815102…76532109373511873281
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
2.694 Γ— 10⁹⁡(96-digit number)
26944686622643630204…53064218747023746559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.694 Γ— 10⁹⁡(96-digit number)
26944686622643630204…53064218747023746561
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
5.388 Γ— 10⁹⁡(96-digit number)
53889373245287260408…06128437494047493119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.388 Γ— 10⁹⁡(96-digit number)
53889373245287260408…06128437494047493121
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
1.077 Γ— 10⁹⁢(97-digit number)
10777874649057452081…12256874988094986239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.077 Γ— 10⁹⁢(97-digit number)
10777874649057452081…12256874988094986241
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
2.155 Γ— 10⁹⁢(97-digit number)
21555749298114904163…24513749976189972479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.155 Γ— 10⁹⁢(97-digit number)
21555749298114904163…24513749976189972481
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:57,840,223 XPMΒ·at block #6,824,519 Β· updates every 60s
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