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Block #2,169,814

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2017, 3:38:37 AM Β· Difficulty 10.9007 Β· 4,674,794 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8ca90e366b84cce7e07d070eb0ed135a0281be536bb40b6eaf4031817d44d3d5
View on Chainz β†—

Height

#2,169,814

Difficulty

10.900746

Transactions

1

Size

200 B

Version

2

Bits

0ae69750

Nonce

294,139,070

Timestamp

6/21/2017, 3:38:37 AM

Confirmations

4,674,794

Mined by

⛏️ P2SHAYW6ezDDYd8G7DJqXdPzDbjyEWC8fJ3WiR

Merkle Root

5677c9172c38ed96b2a6fe5a147af9721242069530289cfe06631667272a1e86
Transactions (1)
Coinbase5677c9172c38ed…631667272a1e86
1 in β†’ 1 out8.4000 XPM110 B
AYW6ezDD…C8fJ3WiR
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.

6.581 Γ— 10⁹⁴(95-digit number)
65819147093822369660…54137048063691612159
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
6.581 Γ— 10⁹⁴(95-digit number)
65819147093822369660…54137048063691612159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.581 Γ— 10⁹⁴(95-digit number)
65819147093822369660…54137048063691612161
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
1.316 Γ— 10⁹⁡(96-digit number)
13163829418764473932…08274096127383224319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.316 Γ— 10⁹⁡(96-digit number)
13163829418764473932…08274096127383224321
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
2.632 Γ— 10⁹⁡(96-digit number)
26327658837528947864…16548192254766448639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.632 Γ— 10⁹⁡(96-digit number)
26327658837528947864…16548192254766448641
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
5.265 Γ— 10⁹⁡(96-digit number)
52655317675057895728…33096384509532897279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.265 Γ— 10⁹⁡(96-digit number)
52655317675057895728…33096384509532897281
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
1.053 Γ— 10⁹⁢(97-digit number)
10531063535011579145…66192769019065794559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.053 Γ— 10⁹⁢(97-digit number)
10531063535011579145…66192769019065794561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.106 Γ— 10⁹⁢(97-digit number)
21062127070023158291…32385538038131589119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,001,267 XPMΒ·at block #6,844,607 Β· updates every 60s
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