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Block #2,130,505

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 11:36:16 AM Β· Difficulty 10.9097 Β· 4,703,205 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
027f7c555cd0c3245c726e8a1cd02e5b2f754b5133cb74fa898dda335948c1fe
View on Chainz β†—

Height

#2,130,505

Difficulty

10.909659

Transactions

2

Size

538 B

Version

2

Bits

0ae8df6e

Nonce

871,419,688

Timestamp

5/24/2017, 11:36:16 AM

Confirmations

4,703,205

Mined by

⛏️ P2SHAacjvRpdGUp4afgqzTGTgSNjS3M7mfCkkM

Merkle Root

98f4bb69c4b4854b0bfb87faf41ac4cb383e22cd0e8f1dca9f06044d17296d32
Transactions (2)
Coinbase77d6b6c6871c74…59d6a8bd5bc99b
1 in β†’ 1 out8.4000 XPM109 B
AacjvRpd…M7mfCkkM
21e5a07fc80dc0…bcb7c589bd40c4
2 in β†’ 1 out999.9900 XPM339 B
APWifXPe…RFN36sad
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.

1.350 Γ— 10⁹⁴(95-digit number)
13507927769932233938…82742852552237552319
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
1.350 Γ— 10⁹⁴(95-digit number)
13507927769932233938…82742852552237552319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.350 Γ— 10⁹⁴(95-digit number)
13507927769932233938…82742852552237552321
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
2.701 Γ— 10⁹⁴(95-digit number)
27015855539864467877…65485705104475104639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.701 Γ— 10⁹⁴(95-digit number)
27015855539864467877…65485705104475104641
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
5.403 Γ— 10⁹⁴(95-digit number)
54031711079728935754…30971410208950209279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.403 Γ— 10⁹⁴(95-digit number)
54031711079728935754…30971410208950209281
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
1.080 Γ— 10⁹⁡(96-digit number)
10806342215945787150…61942820417900418559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.080 Γ— 10⁹⁡(96-digit number)
10806342215945787150…61942820417900418561
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
2.161 Γ— 10⁹⁡(96-digit number)
21612684431891574301…23885640835800837119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.161 Γ— 10⁹⁡(96-digit number)
21612684431891574301…23885640835800837121
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
4.322 Γ— 10⁹⁡(96-digit number)
43225368863783148603…47771281671601674239
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:57,913,901 XPMΒ·at block #6,833,709 Β· updates every 60s
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