Block #2,027,020

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/17/2017, 2:18:45 PM · Difficulty 10.7099 · 4,806,573 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9aa8cd2686f2ed3d67018d83a18582bb97f6b731ee0b96bd8a4ff63800cbd151

View on Chainz ↗

Height

#2,027,020

Difficulty

10.709868

Transactions

Size

12.12 KB

Version

Bits

0ab5b9e4

Nonce

995,769,751

Timestamp

3/17/2017, 2:18:45 PM

Confirmations

4,806,573

Mined by

⛏️ P2SHAKa9SVziMEVuuopprpZXZ8FHrgMKFdhTbB

Merkle Root

fdfca2a64bb9a77dc45fefc984f9bed6622af42bb465b8f56295bbe38e9705ce

Transactions (2)

Coinbasea8a9c2ef0b4ef8…4c69e5dd69c550

1 in → 1 out8.9000 XPM109 B

AKa9SVzi…MKFdhTbB

3845b8320c1192…aef91c1b56c13b

82 in → 2 out56.2140 XPM11.92 KB

AbhnvSYn…Du1vySkV ATCnCKAe…DRPnfPxf

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.876 × 10⁹⁵(96-digit number)

58767961502794061162…78963816130421340159

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

5.876 × 10⁹⁵(96-digit number)

58767961502794061162…78963816130421340159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.876 × 10⁹⁵(96-digit number)

58767961502794061162…78963816130421340161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.175 × 10⁹⁶(97-digit number)

11753592300558812232…57927632260842680319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.175 × 10⁹⁶(97-digit number)

11753592300558812232…57927632260842680321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.350 × 10⁹⁶(97-digit number)

23507184601117624465…15855264521685360639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.350 × 10⁹⁶(97-digit number)

23507184601117624465…15855264521685360641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.701 × 10⁹⁶(97-digit number)

47014369202235248930…31710529043370721279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.701 × 10⁹⁶(97-digit number)

47014369202235248930…31710529043370721281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

9.402 × 10⁹⁶(97-digit number)

94028738404470497860…63421058086741442559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.402 × 10⁹⁶(97-digit number)

94028738404470497860…63421058086741442561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.880 × 10⁹⁷(98-digit number)

18805747680894099572…26842116173482885119

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,027,020

Cookie Preferences