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Block #1,898,018

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2016, 8:42:53 AM Β· Difficulty 10.7537 Β· 4,946,969 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb3fd940fc90de93539b54b3531e10981b64d3a9cf0d4265815789245ae59a49
View on Chainz β†—

Height

#1,898,018

Difficulty

10.753664

Transactions

2

Size

12.71 KB

Version

2

Bits

0ac0f021

Nonce

118,978,786

Timestamp

12/17/2016, 8:42:53 AM

Confirmations

4,946,969

Mined by

⛏️ P2SHASCvtH6xZyFNuUWDye4PMraDNVMMEdnTo2

Merkle Root

0ac7d0fb420c9257a228fe1966577ae0a21d7a7e71d63c2cacc88edae958a0e4
Transactions (2)
Coinbased26a74b66d6750…80ddc506e4ad1c
1 in β†’ 1 out8.7600 XPM109 B
ASCvtH6x…MMEdnTo2
6629159fb6c28a…757ba7d2be8ad3
86 in β†’ 2 out2605.5605 XPM12.52 KB
AdUbFbQ9…MXLm2P1GANJHs6uD…VD75ysYL
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.

9.362 Γ— 10⁹⁴(95-digit number)
93623148278354577183…09182660999484802879
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
9.362 Γ— 10⁹⁴(95-digit number)
93623148278354577183…09182660999484802879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.362 Γ— 10⁹⁴(95-digit number)
93623148278354577183…09182660999484802881
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
1.872 Γ— 10⁹⁡(96-digit number)
18724629655670915436…18365321998969605759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.872 Γ— 10⁹⁡(96-digit number)
18724629655670915436…18365321998969605761
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
3.744 Γ— 10⁹⁡(96-digit number)
37449259311341830873…36730643997939211519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.744 Γ— 10⁹⁡(96-digit number)
37449259311341830873…36730643997939211521
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
7.489 Γ— 10⁹⁡(96-digit number)
74898518622683661746…73461287995878423039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.489 Γ— 10⁹⁡(96-digit number)
74898518622683661746…73461287995878423041
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
1.497 Γ— 10⁹⁢(97-digit number)
14979703724536732349…46922575991756846079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.497 Γ— 10⁹⁢(97-digit number)
14979703724536732349…46922575991756846081
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:58,004,315 XPMΒ·at block #6,844,986 Β· updates every 60s
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