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Block #2,125,569

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/20/2017, 3:59:02 PM Β· Difficulty 10.9190 Β· 4,719,360 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
80cff66d566132dcec50db50613e481ac9d5064b2a35ff23f227347d9bcafa2b
View on Chainz β†—

Height

#2,125,569

Difficulty

10.918990

Transactions

2

Size

393 B

Version

2

Bits

0aeb42f6

Nonce

395,909,872

Timestamp

5/20/2017, 3:59:02 PM

Confirmations

4,719,360

Mined by

⛏️ P2SHAZ77rrm8x872pE1PpcFo1YKibJHJStscdL

Merkle Root

1817d70ee4cd19a8901f5c760f8d30bef225ba1d2349861f7b51c310a89aa30c
Transactions (2)
Coinbase34ea775b45e95d…ae0ed667b1c484
1 in β†’ 1 out8.3800 XPM109 B
AZ77rrm8…HJStscdL
85e12eadfea703…28fd227638d587
1 in β†’ 1 out99.9900 XPM193 B
ARsuhVkc…w3M6D8DV
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.

5.834 Γ— 10⁹⁷(98-digit number)
58340252450556332122…16477507048292638719
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
5.834 Γ— 10⁹⁷(98-digit number)
58340252450556332122…16477507048292638719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.834 Γ— 10⁹⁷(98-digit number)
58340252450556332122…16477507048292638721
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
1.166 Γ— 10⁹⁸(99-digit number)
11668050490111266424…32955014096585277439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.166 Γ— 10⁹⁸(99-digit number)
11668050490111266424…32955014096585277441
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
2.333 Γ— 10⁹⁸(99-digit number)
23336100980222532849…65910028193170554879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.333 Γ— 10⁹⁸(99-digit number)
23336100980222532849…65910028193170554881
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
4.667 Γ— 10⁹⁸(99-digit number)
46672201960445065698…31820056386341109759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.667 Γ— 10⁹⁸(99-digit number)
46672201960445065698…31820056386341109761
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
9.334 Γ— 10⁹⁸(99-digit number)
93344403920890131396…63640112772682219519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.334 Γ— 10⁹⁸(99-digit number)
93344403920890131396…63640112772682219521
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
1.866 Γ— 10⁹⁹(100-digit number)
18668880784178026279…27280225545364439039
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:58,003,849 XPMΒ·at block #6,844,928 Β· updates every 60s
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