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Block #1,510,057

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/24/2016, 7:33:29 AM Β· Difficulty 10.6161 Β· 5,314,743 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b243edb34e47d131851c4884f457337a1de2f29f7e1c5cc47a737680a5b22944
View on Chainz β†—

Height

#1,510,057

Difficulty

10.616140

Transactions

2

Size

428 B

Version

2

Bits

0a9dbb53

Nonce

1,162,735,572

Timestamp

3/24/2016, 7:33:29 AM

Confirmations

5,314,743

Mined by

⛏️ P2SHAX2vsTs14JzUWCj3u87WKunkjg9G7f1NBN

Merkle Root

f92d74ac71fc8721fca2481b38392ac84491e5fb3cbb79b87cc49cf327e5dab3
Transactions (2)
Coinbase09696cbf053725…5428b1e3c2d0b2
1 in β†’ 1 out8.8700 XPM110 B
AX2vsTs1…9G7f1NBN
e558b52be00c8f…923d01c76bc7c5
1 in β†’ 2 out0.1300 XPM227 B
AX8SRCbJ…87twGEaBARUKNyfN…dMYZekay
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.

2.752 Γ— 10⁹⁢(97-digit number)
27521047731649405510…61760467400549253119
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
2.752 Γ— 10⁹⁢(97-digit number)
27521047731649405510…61760467400549253119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.752 Γ— 10⁹⁢(97-digit number)
27521047731649405510…61760467400549253121
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
5.504 Γ— 10⁹⁢(97-digit number)
55042095463298811021…23520934801098506239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.504 Γ— 10⁹⁢(97-digit number)
55042095463298811021…23520934801098506241
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
1.100 Γ— 10⁹⁷(98-digit number)
11008419092659762204…47041869602197012479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.100 Γ— 10⁹⁷(98-digit number)
11008419092659762204…47041869602197012481
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
2.201 Γ— 10⁹⁷(98-digit number)
22016838185319524408…94083739204394024959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.201 Γ— 10⁹⁷(98-digit number)
22016838185319524408…94083739204394024961
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
4.403 Γ— 10⁹⁷(98-digit number)
44033676370639048817…88167478408788049919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.403 Γ— 10⁹⁷(98-digit number)
44033676370639048817…88167478408788049921
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:57,842,475 XPMΒ·at block #6,824,799 Β· updates every 60s
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