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Block #1,960,571

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/29/2017, 11:43:57 PM Β· Difficulty 10.7427 Β· 4,876,224 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b38d300235b2b87d060a1f2edc5c1e2900e4c004ec601e216a307d5e54d7cb6b
View on Chainz β†—

Height

#1,960,571

Difficulty

10.742727

Transactions

1

Size

201 B

Version

2

Bits

0abe2355

Nonce

630,501,832

Timestamp

1/29/2017, 11:43:57 PM

Confirmations

4,876,224

Mined by

⛏️ P2SHAP54BTzw75GYw2Bdjhz4ScJZLqURxQgsp6

Merkle Root

65bb7a8e668a7078929cf90d3110f3759e1318c5a65f84f4364c947aac7fcbd1
Transactions (1)
Coinbase65bb7a8e668a70…4c947aac7fcbd1
1 in β†’ 1 out8.6500 XPM110 B
AP54BTzw…URxQgsp6
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.

8.760 Γ— 10⁹⁷(98-digit number)
87607187969830667423…26189416233555537919
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
8.760 Γ— 10⁹⁷(98-digit number)
87607187969830667423…26189416233555537919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.760 Γ— 10⁹⁷(98-digit number)
87607187969830667423…26189416233555537921
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
1.752 Γ— 10⁹⁸(99-digit number)
17521437593966133484…52378832467111075839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.752 Γ— 10⁹⁸(99-digit number)
17521437593966133484…52378832467111075841
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
3.504 Γ— 10⁹⁸(99-digit number)
35042875187932266969…04757664934222151679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.504 Γ— 10⁹⁸(99-digit number)
35042875187932266969…04757664934222151681
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
7.008 Γ— 10⁹⁸(99-digit number)
70085750375864533938…09515329868444303359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.008 Γ— 10⁹⁸(99-digit number)
70085750375864533938…09515329868444303361
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
1.401 Γ— 10⁹⁹(100-digit number)
14017150075172906787…19030659736888606719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.401 Γ— 10⁹⁹(100-digit number)
14017150075172906787…19030659736888606721
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:57,938,641 XPMΒ·at block #6,836,794 Β· updates every 60s
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