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Block #2,162,753

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2017, 5:52:15 AM Β· Difficulty 10.9007 Β· 4,671,251 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
62c8cf7e8ef430e8a8d6b5ef08e5125659bd68c1c389fa35977b31bcf94cf0f7
View on Chainz β†—

Height

#2,162,753

Difficulty

10.900656

Transactions

2

Size

5.87 KB

Version

2

Bits

0ae69167

Nonce

1,229,789,962

Timestamp

6/16/2017, 5:52:15 AM

Confirmations

4,671,251

Mined by

⛏️ P2SHAZeMKNCgQToq6yoxP1dFhyfo1HJc4trUCp

Merkle Root

c01b28ec1c52a7cce2e7ee34582b8ec7962cf38642441d37bcb90cb77b9941c4
Transactions (2)
Coinbase72a8af01c94123…0ea9b6d2b87139
1 in β†’ 1 out8.4600 XPM110 B
AZeMKNCg…Jc4trUCp
456c88925406a8…112eb21a04fa38
39 in β†’ 1 out278.9080 XPM5.67 KB
ANR6yEBj…xx5Lorbw
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.

1.767 Γ— 10⁹⁴(95-digit number)
17671530765850616350…47474333653119607719
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
1.767 Γ— 10⁹⁴(95-digit number)
17671530765850616350…47474333653119607719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.767 Γ— 10⁹⁴(95-digit number)
17671530765850616350…47474333653119607721
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
3.534 Γ— 10⁹⁴(95-digit number)
35343061531701232700…94948667306239215439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.534 Γ— 10⁹⁴(95-digit number)
35343061531701232700…94948667306239215441
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
7.068 Γ— 10⁹⁴(95-digit number)
70686123063402465400…89897334612478430879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.068 Γ— 10⁹⁴(95-digit number)
70686123063402465400…89897334612478430881
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
1.413 Γ— 10⁹⁡(96-digit number)
14137224612680493080…79794669224956861759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.413 Γ— 10⁹⁡(96-digit number)
14137224612680493080…79794669224956861761
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
2.827 Γ— 10⁹⁡(96-digit number)
28274449225360986160…59589338449913723519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.827 Γ— 10⁹⁡(96-digit number)
28274449225360986160…59589338449913723521
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:57,916,259 XPMΒ·at block #6,834,003 Β· updates every 60s
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