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Block #1,649,239

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/28/2016, 4:36:52 PM Β· Difficulty 10.6513 Β· 5,167,886 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe25399d39a9fce7380fd7771b354c9ad20a7842e16b4accf23572de39bb87d6
View on Chainz β†—

Height

#1,649,239

Difficulty

10.651301

Transactions

2

Size

6.19 KB

Version

2

Bits

0aa6bbab

Nonce

927,491,045

Timestamp

6/28/2016, 4:36:52 PM

Confirmations

5,167,886

Mined by

⛏️ P2SHAVEYR9RxCtSY1jdrHcSK1fJn4rZSes9tW5

Merkle Root

a1458ed02645df0a17907187074c7f6abb6a2bcbaca3d9f5f499777dae1d8aff
Transactions (2)
Coinbasedac2dce542a6c1…e1072bffb1317e
1 in β†’ 1 out8.8700 XPM109 B
AVEYR9Rx…ZSes9tW5
a702415ad17a3f…1d3bc5c8add1af
41 in β†’ 2 out4.8967 XPM6.00 KB
AZ5UqnLG…qhGCrkn2AcXDnG1h…zL6LZ3ao
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.

1.914 Γ— 10⁹⁴(95-digit number)
19147447753424898985…48518483093839973119
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
1.914 Γ— 10⁹⁴(95-digit number)
19147447753424898985…48518483093839973119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.914 Γ— 10⁹⁴(95-digit number)
19147447753424898985…48518483093839973121
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
3.829 Γ— 10⁹⁴(95-digit number)
38294895506849797970…97036966187679946239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.829 Γ— 10⁹⁴(95-digit number)
38294895506849797970…97036966187679946241
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
7.658 Γ— 10⁹⁴(95-digit number)
76589791013699595941…94073932375359892479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.658 Γ— 10⁹⁴(95-digit number)
76589791013699595941…94073932375359892481
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
1.531 Γ— 10⁹⁡(96-digit number)
15317958202739919188…88147864750719784959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.531 Γ— 10⁹⁡(96-digit number)
15317958202739919188…88147864750719784961
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
3.063 Γ— 10⁹⁡(96-digit number)
30635916405479838376…76295729501439569919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.063 Γ— 10⁹⁡(96-digit number)
30635916405479838376…76295729501439569921
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:57,781,033 XPMΒ·at block #6,817,124 Β· updates every 60s
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